Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 2x + 6$ and $ KL = 6x - 14$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {2x + 6} = {6x - 14}$ Solve for $x$ $ -4x = -20$ $ x = 5$ Substitute $5$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 2({5}) + 6$ $ KL = 6({5}) - 14$ $ JK = 10 + 6$ $ KL = 30 - 14$ $ JK = 16$ $ KL = 16$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {16} + {16}$ $ JL = 32$